43 to 40, and agrees with me to play till 100
stakes are won or lost on either side, on condition that I give him
an equivalent for the gain I am entitled to by the advantage of my
odds;--the question is, what I am to give him, supposing we play at a
guinea a stake? The answer is 99 guineas and above 18 shillings,(52)
which will seem almost incredible, considering the smallness of the
odds--43 to 40. Now let the odds be in any proportion, and let
the number of stakes played for be never so great, yet one general
conclusion will include all the possible cases, and the application of
it to numbers may be worked out in less than a minute's time.'(53)

(52) The guinea was worth 21s. 6d. when the work quoted was written.

(53) De Moivre, Doctrine of Chances.

The possible combinations of cards in a hand as dealt out by chance are
truly wonderful. It has been established by calculation that a player
at Whist may hold above 635 thousand millions of various hands! So that,
continually varied, at 50 deals per evening, for 313 evenings, or 15,650
hands per annum, he might be above 40 millions of years before he would
have the same hand again!

The chance is equal, in dealing cards, that every hand will have seven
trumps in two deals, or seven trumps between two partners, and also four
court cards in every deal. It is also certain on an average of hands,
that nothing can be more superstitious and absurd than the prevailing
notions about luck or ill-luck. Four persons, constantly playing at
Whist during a long voyage, were frequently winners and losers to
a large amount, but as frequently at 'quits;' and at the end of the
voyage, after the last game, one of them was minus only one franc!

The chance of having a particular card out of 13 is 13/52, or 1 to
4, and the chance of holding any two cards is 1/4 of 1/4 or 1/16. The
chances of a game are generally inversely as the number got by each, or
as the number to be got to complete each game.

The chances against holding seven trumps are 160 to 1; against six, it
is 26 to 1; against five, 6 to 1; and against four nearly 2 to 1. It is
8 to 1 against holding any two particular cards.

Similar calculations have been made respecting the probabilities with
dice. There are 36 chances upon two dice.

It is an even chance that you throw 8. It is 35 to 1 against throwing
any particular doublets, and 6 to 1 against any doublets at all. It is
17 to 1 against throwing any two desired